Transmission systems and decoders therefor

ABSTRACT

Digital data is processed by quantizing the data to produce samples, each with a most significant bits and least significant bits with the least significant bits representing reliabilities, generating a parities from the most significant bits of the samples, generating weight functions corresponding to the parities on the basis of the number of times a reliability measure occurs, and producing a corrected stream of data with the weight functions and the corresponding parities.

BACKGROUND OF THE INVENTION

This invention relates to communication and other data transfer systems and to decoders therefor, and particularly to systems and decoders using soft decisions for decoding convolutional and block codes.

Communication and other data transfer systems employ error correction decoders to enhance the accuracy of the received information. In such systems the use of soft decision decoding of convolutional and block codes improves the error correction capability of a particular code. One technique of soft decision decoding is the optimum symbol-by-symbol decoding method disclosed in the article of C. R. P. Hartman, and L. D. Rudolph, entitled "An Optimum Symbol-by-Symbol Decoding Rule for Linear Codes," in the IEEE Transactions on Information Theory, IT-22, 514-517, September 1976. Another technique is a priori probabilistic (APP) decoding disclosed in the book "Threshold Decoding", by J. L. Massey, MIT Press 1963, Cambridge, Massachusetts.

The optimum symbol-by-symbol decoding technique uses soft decisions for decoding any block code whereas the APP decoding approach is suitable for threshold decodable codes, which may be block codes or convolutional codes. Threshold decodable codes are very helpful because of the simplicity of their implementations. However, the exact weight function needed to benefit from soft decisions in either the optimum symbol-by-symbol decoding operation or the exact APP decoding method is highly non-linear and very complex to implement when the block length or the constraint length is large. Hence it is practical to apply a simple approximation of the weight function that can give a good coding gain.

Previously known simple approximations of the weight function for soft decision decoding appear in the article of H. Tanaka, K. Furusawa, and S. Kaneku entitled "A Novel Approach to Soft Decision Decoding of Threshold Decodable Codes", IT-26, 244-246, March 1980. However, these fail to obtain the possible coding gain when the block code is long, i.e. has large block length, or if the constraint length of the convolutional code is long.

OBJECTS AND SUMMARY OF THE INVENTION

An object of this invention is to improve communication systems and error correction decoders.

Another object is to furnish such systems and error correction decoders with a simple, easily implemented weight function.

According to a feature of the invention, such objects are attained by generating a number of parity checks from the most significant bits of quantized data samples of signals that have passed through a transmission channel of a communication system, and generating weight functions corresponding to the parity checks on the basis of the number of times a reliability measure occurs. This results in an improved soft decision decoder.

Another aspect of the invention involves decoding the output of a soft decision decoder that uses weight functions based on the number of times a reliability measure occurs.

These and other features of the invention are pointed out in the claims. Other objects and advantages of the invention will become evident from the following detailed description when read in light of the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. a block diagram of a system embodying features of the invention.

FIG. 2 is a block diagram of a decoder in FIG. 1 and also embodying features of the invention

FIG. 3 is a block diagram of a parity generator in FIG. 2.

FIG. 4 is a block diagram of a weight function generator in FIG. 2.

FIGS. 5 and 6 are logic and block diagrams showing details of portions of FIG. 2.

FIGS. 7A to 7C are block and circuit diagrams showing details of portions of FIG. 2.

FIG. 8 is a partial block and logic diagram showing a communication system embodying features of the invention and including a weight function circuit according to the invention.

FIG. 9 is a block diagram illustrating details of a transmitter shown in FIG. 1.

FIG. 10 is a block diagram showing an output circuit forming part of a receiver in FIG. 1.

FIG. 11 is a block diagram of a transmission system depicting a combination of circuitry in FIGS. 1, 2, and 3.

FIG. 12 is a block diagram of another system embodying the features of FIG. 1.

FIG. 13 is a diagram illustrating the arrangement in FIG. 1 that generates the parities in FIG. 1.

FIGS. 14 and 15 are other embodiments of portions of the circuit in FIG. 2.

FIG. 16 is yet another embodiment of portions of the circuit in FIG. 2.

FIGS. 17, 18, 19, and 20 illustrate still other embodiments of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In the communication system of FIG. 1, a transmitter TR₁ transmits digital data through a communication channel CC₁ to a receiver RE₁. The receiver RE₁ includes a demodulator DM₁, a storage buffer SB₁, a decoder DE₁, and an output circuit OC₁.

In FIG. 1, the demodulator DE₁ extracts samples from the data and quantizes each extracted sample to Q bits, for example 3 bits. The most significant bits (MSB) in a sample from the demodulator DE₁ represent the hard decision and the least significant bits (LSB) represent the magnitude, or the reliability, of the sample. In a general case of Q bits, the first bit is used as the most significant bit and the last Q-1 bits the reliabilities. The storage buffer SB₁ stores the MSB's and LSB's of successive blocks of samples for application by block to the decoder DE₁.

Components of the decoder DE₁, appear in FIG. 2. Here a parity generator PG₁ receives the MSB's of samples in a block of data and generates J+1 parities B_(o) to B_(J). A weight function generator WG₁ receives the LSB's of the samples in a block of data and generates J+1 weight functions W_(o) to W_(J). A mapping circuit MC₁, weights and maps the parities B_(o) to B_(J) with the weight functions W_(o) to W_(J) to produce weighted parities (2B₀ -1)W₀ to (2B_(J) -1)W_(J) which enter the inputs of a full adder FA₁. The latter forms a decision variable F. A comparator CO₁ compares the value F with 0 to produce a value C_(m) to establish a value 1 or 0. The value 1 or 0 passes to the output circuit OC₁ either directly or through a second buffer.

The generators PG₁ and WG₁ repeat the process with the mapping circuit MC₁, the full adder FA₁, and the comparator CO₁, for all the samples. The resulting bits also pass to the output circuit OC₁ either directly or through the second buffer. When the bits representing all the samples have been shifted, the buffer SB₁ applies the MSB's and LSB's of samples in a new block to the respective generators PG₁ and WG₁.

Details of the parity generator PG₁ appear in FIG. 3. Here, to generate J parities, a select switch SE₁ composed of two or more gates (not shown) selects n MSB's of a block of n samples stored in the buffer SB₁ and feeds them into an n stage shift register SR₁ with stages S₀ to S.sub.(n-1). Thereafter, the select switch SE₁ selects, i.e. connects to, a feedback path. In the first decoding cycle, after feeding of the MSB's in samples to the shift register SR₁, a reordering circuit OC₁ connects the stages S₀ to S.sub.(n-2) to J sets of multiple input exclusive OR circuits XO₁ to XO_(J). The latter forms J parities B₁ to B_(J). The stage S.sub.(n-1) forms parity B₀. Hence the system produces (J+1) parities B₀ to B_(J) from the n MSB's.

Reordering circuits of S_(j), where j=1 to n, are known and have connections based on known codes. Further details of circuits such as SE₁, SR₁, RC₁, XO₁ to XO_(J) appear in more detail in FIG. 13. The operation of such circuits is described in the book "Error Control Coding; Fundamentals and Applications", by Lin and Costello, page 208. The description is rendered in terms applicable to block code. This is only illustrative and the invention is usable with other codes, such as threshold decodable convolution codes.

FIG. 4 illustrates the weight function generator WG₁. Here, at the same time that the selector switch SE₁ supplies the n MSB's to the shift register SR₁ from the demodulator DE₁, a selector switch SE₂ furnishes the corresponding Q-1 LSB's from each of the n samples to a shift register SR₂ whose length is (Q-1)*n bits. Thus the shift register SR₂ receive n*(Q-1) LSB's from the block of samples.

A reorder circuit RC₂ reorders the first (Q-1) * (n-1) outputs at the stages S₀ to S.sub.[(n-1)(Q-1)-1] of the shift register SR₂ into J sets SE₁ to SE_(J) of m*(Q-1) outputs each. The number m is a parameter of the known code (see Lin and Costello supra) and is the number of components in the parity equation for which the weight function is being determined. Each of the sets is divided into Q-1 groups of m binary elements. The m signals (Q-1) groups of J sets enter the inputs of J weight function circuits WF₁ to WF_(J). The latter produce J weight functions W₁ to W_(J) each corresponding to the analogous one of the J parities B₁ to B_(J).

The last Q-1 stages, stages S.sub.[(n-2)(Q-1)] to S.sub.(n-1)(Q-1)-1], of the shift register supply a weight function circuit WF₀. The latter produces a weight W₀ corresponding to the parity B₀.

The parities B₀ to B_(J) of FIGS. 2 and 3 have levels of either 0 or 1. The mapping circuit MC₁ maps the parities B₀ to B_(J) as shown in FIGS. 7A, 7B, and 7C. Each of the weights W_(i) is inverted if B_(i) equals 0 and is not inverted if B_(i) =1 (i=0 to J). This produces weighted parities (2B₀ -1) W₀, (2B₁ -1) W₁, . . . (2B_(J) -1) W_(J).

The full adder FA₁ of FIG. 2 sums the weighted parities (2B₀ -1) W₀, (2B₁ -1) W₁, . . . (2B_(J) -1) W_(J) to obtain a decision variable F. The comparator C0₁ compares the value of F with 0 to produce a value C_(m) representing the decode orthogonal bit. If the value F>0, then C_(m) is 1, if F<0, then C_(m) is 0.

Upon completion of the operation by the comparator C0₁, the sampled data is shifted cyclically one bit to the right.

The above circuitry of FIGS. 1 to 4 repeats the aforementioned process to decode a different bit of the code word. The new bit formed is now the orthogonal code bit. The system repeats the process n times to decode the entire code word. After decoding the entire code word, the select switches SE₁ and SE₂ enter a new code word into the shift register SR₁ and SR₂. Suitable memories in the demodulator and the output circuit store the samples and orthogonal bits as needed.

The circuit of FIGS. 1 to 4 improves the operation of the communication system and the efficiency of the decoding by virtue of the operation of the weight function circuits WF₀ to WF_(J). The latter determine not only the least reliable component of the weights W₀ to W_(J), i.e. the minimum of the n outputs, but also the number of occurrences of the minimum value.

FIGS. 5 and 6 exhibit details of the weight function circuit WF_(J), which is identical to and representative of the circuits WF₀ to WF_(J). As noted from FIG. 4, each weight function circuit WF₁ to WF_(J) receives (Q-1)*m samples from the reorder circuit RC₂. As shown in FIG. 5, Q is assumed to be 3, and the inputs to the weight function circuit WF_(J) are regrouped from m groups of Q-1 inputs as shown in FIG. 4, to Q-1 groups of m inputs each. The first group of m inputs carries the name a₁, and the second group of m inputs bears the designation a₂. This arises because if we assume Q=3, each of the n received samples is represented by a 3 bit number a₀, 1, and a₂ one of which, a₀, is the hard decision in the sample. Accordingly, the remaining two bits a₁ and a₂ in the sample represent the reliabilities or soft decision. Thus, the output of the reorder circuit OC₁ to the weight function WF_(J) is in the form of m samples a₁ and a₂. The magnitude of each of the m samples is a₁ a₂ for that sample. These are regrouped in the form of m inputs a₁, a₂.

The values of the m components a₁ constitute the input of an AND gate AD₁ as well the inputs of respective exclusive OR gates XR₁, XR₂, . . . XR_(m). The output M₁ of the AND gate AD₁ is 0 if any one of the four inputs a₁ to the AND gate AD₁ is 0. If all of the inputs to the AND gate AD₁ are 1, M₁ equals 1.

The value 0 or 1 of M₁ at the output of the AND gate AD₁ forms the input of m exclusive OR gates XR₁, XR₂, . . . XR_(m). When M₁ is 1, the output of the exclusive OR gates are all zeros because all the values a₁ are also 1. When M₁ is zero, then the output of each corresponding exclusive OR gate XR₁, XR₂, . . . XR_(m) is the value a₁ of the corresponding sample.

The outputs A₁, A₂, . . . A_(m) of the exclusive OR gates XR₁, XR₂, . . . XR_(m) appear at the inputs of OR gates OR₁, OR₂, . . . OR_(m). The other inputs to the latter OR gates are the m values a₂. Hence, when M₁ is 1, the output of the exclusive OR gates XR₁ to XR_(m) are all zeros and hence the outputs of the OR gates OR₁, OR₂, . . . OR_(m) represent the m values a₂.

When M₁ is 0, the inputs to the OR gates OR₁, OR₂, . . . OR_(m) from the exclusive OR gates XR₁ to XR_(m) correspond to the m values of a₁. The other inputs to the OR gates OR₁, OR₂, . . . OR₁ represent the m values of a₂. Then each output of the OR gates OR₁ to OR_(m) is a 1 unless a corresponding pair of a₁ and a₂ is 0.

The OR gates OR₁, OR₂, . . . OR_(m) pass the signals applied thereto to an AND gate AD₂ having an output M₂. If M₁ is 1 because all m a₁ values are 1 and hence all exclusive OR gates XR₁ to XR_(m) are 0, the AND gate AD₂ goes to 1 only if all values a₂ are 1 and goes to 0 if any one of the values a₂ is 0.

On the other hand if M₁ is 0 because at least one value a₁ is 0, and hence the outputs of the exclusive OR gates XR₁ to XR_(m) correspond to the m values a₁, then the AND gate AD₂ produces a 1 unless a corresponding pair of values a₁ and a₂ is 0.

In effect, if M₁ is 1, the circuitry ANDs, the components a₂ to obtain M₂. If M₁ is zero, then the circuit logically ANDs only the values a₂ whose components a₁ in the sample are 0.

As shown in FIG. 6, the output M₂ passes to the inputs of m exclusive OR gates Xr₁, Xr₂, . . . Xr_(m) which also receive the m respective values a₂. These gates indicate at their respective outputs X₁, X₂, . . . X_(m) whether the value M₂ corresponds to the values of a₂. A similar determination occurred at the outputs A₁ to A_(m) which denoted whether M₁ corresponds to the values a₁. The plurality m NOR gates Nr₁, Nr₂, . . . Nr_(m) receive respective values A₁ to A_(m) and values X₁ to X_(m) to determine whether they differ or not, and hence whether M₁ M₂ equals a₁ a₂ or not. An adder DD₁ adds the outputs U₁ to U_(m) of gates Nr₁ to Nr_(m) to obtain the number N of times the minimum occurs.

A read only memory (ROM) RM₁ receives the output M₁ at the output of the AND gate AD₁, the value M₂ at the AND gate AD₂, and the number N from the adder DD₁ to produce the weight W_(J). The ROM RM₁ establishes the minimum |y_(min) | which represents the digital value of the values M₁ and M₂. It then produces an output W_(J) based on the following look-up table. This look-up table is, for an example, for the (21, 11) threshold decodable block code, J=5, m=4.

                  TABLE 1                                                          ______________________________________                                         M.sub.1  M.sub.2                                                                              |y.sub.min |                                                               N   output W                                      ______________________________________                                         0        0     0             4    1                                            0        0     0             3    2                                            0        0     0             2    4                                            0        0     0             1    8                                            0        1     1             4   14                                            0        1     1             3   16                                            0        1     1             2   19                                            0        1     1             1   24                                            1        0     2             4   30                                            1        0     2             3   32                                            1        0     2             2   35                                            1        0     2             1   40                                            1        1     3             4   50                                            ______________________________________                                          ##STR1##                                                                 

FIGS. 7A to 7C illustrate a mapping circuit embodying the invention. FIG. 7B shows details of FIG. 7A, and the latter is a shorthand version of FIG. 7B. Here multiplexers MUX_(i), where i=0 . . . J, receive the value W_(i) directly and W_(i) through inverters IN_(i). The multiplexers MUX_(i) choose one of inputs W or W depending on whether B is 0 or 1. FIG. 7C illustrates a circuit equivalent of the diagrams in FIG. 7A and 7B. Here the switches B_(i) switch between W_(i) and W_(i).

According to other embodiments of the invention, n can be other lengths such as 273 or 1057 or any shortened version of such codes.

As stated, the weighted parities (2B_(O) -1)W_(O) to (2B_(J) -1)W_(J) enter the inputs of a full adder FA₁. The latter forms a decision variable F. As shown in FIG. 2, the comparator CO₁ compares the value F with 0 to produce a value C_(m) to establish a value 1 or 0. The value 1 or 0 passes to the output circuit OC₁ either directly or through a second buffer.

The select switch SE₁ then circulates the last bit on the right of the register SR₁ to the first position and shifts the content of the register one bit to the right. The select switch SE₂ then circulates the last Q-1 bits of the SR₂ to the entry positions and shifts the content of the register Q-1 bits to the right. This starts the next cycle. The process now repeats until the formation of a new bit C_(m).

When all the cycles have been completed, i.e. the bits representing all the samples have been shifted, the storage buffer SB₁ replaces the MSB's and LSB's of the samples in the shift registers SR₁ and SR₂ with the MSB's and LSB's in a new block. The cycles are then repeated for the new block.

FIG. 8 illustrates a more specific embodiment of the invention wherein Q=3, m=4, and J=5. The circuit elements and operation are otherwise the same as the circuits in FIGS. 1 to 6.

FIG. 9 illustrates the transmitter TR₁ of FIGS. 1 and 7. Here, an analog video generator AV₁ generates analog video signals which enter an analog to digital (A/D) converter ADC. The latter converts the video signals and passes them to a compressor CP₁ which compresses the signals. An encryptor EN₁ encrypts the compressed signals and passes the signals to a forward error correction (FEC) encoder FE₁. A modulator MD₁ then modulates the resulting data stream and sends it to the communication channel.

FIG. 10 shows the output circuit OC₁ which, together with the demodulator DM₁ and the decoder DE₁, forms the receiver of the communication system in FIGS. 1 to 9. The output circuit OC₁ includes a decryptor DY₁ that decrypts the error corrected received data, a decompressor DP₁ for decompressing the decrypted signals, a digital to analog (D/A) converter DAC for reconverting the signal to the analog state, and a display system DS₁ that includes audio and video outputs. The complete system is shown in FIG. 11. Here, like reference characters denote like parts of those in FIGS. 1 to 10, and the like parts perform the same functions.

According to an embodiment of the invention, the systems of FIGS. 9 to 11 do not include the encryptor EN₁, the compressor CP₁, the decrypter DY₁, and the decompressor DP₁. FIG. 12 discloses this arrangement.

FIG. 13 depicts details of an example of a circuit for generating the parities B₀ to B_(J) in FIGS. 2, 3, and 8. Here n=21, a number permitting simple diagramming of the connections. The selector SE₁ enters the MSB's of the quantized samples into the shift register SR₁ with a gate GA₁ while a gate GA₂ holds feedback from the stage S₂₀. When gate GA₂ conducts gate GA₁ is non-conductive. As mentioned the shift register SR₁ has twenty one stages S₀ to S₂₀. Terminals r₀ to r₁₉ of the reorder circuit RC₁ have subscripts identifying the corresponding stages S₀ to S₁₉ to which the reorder circuit connects them. Only some of the connections are portrayed while others are omitted for clarity. The reorder circuit RC₁ collects the connections into five groups of four lines each to exclusive OR (XOR) circuits XO₁ to XO_(J) on the basis of a known predetermined code. The circuits XO₁ to XO_(J) XOR the values to produce parities B₁ to B_(J). The stage S₂₀ itself forms the parity B₀.

The selector SE₂, shift register SR₂, and the reorder circuit RC₂ in FIG. 4 operate in similar manner on the basis of a known code. The final two stages of the shift register SR₂ form the input to the weight function circuit WF₀.

In operation, the demodulator DM₁ receives signal distorted by the channel CH₁ from the transmitter TR₁ and quantizes samples of the signals into Q=3 bits which it applies stores in the storage buffer SB₁. The latter applies them to the decoder DE₁. The MSB becomes the hard decision on the sample and the Q-1=LSB's represent the magnitude of the sample. Hence, if Q=3, there are two possibilities for the hard decision or parity of each sample and the 2^(Q-1) =m=2² =4 possibilities for the magnitude or reliability of each quantized sample. The circuits SE₁, SR₁, RC₁, and XO₁ to XO_(J) form the parities B₀ to B_(J) on the basis of the exclusive OR gates XO₁ to XO_(J). On the other hand, the circuits SE₂, SR₂, RC₂, and WF₁ to WF_(J) implement weight functions W₀ to W_(J) for the parities B₀ to B_(J). Only the magnitudes of the m components of the LSB's determine the weight function. The weight function circuits establish the minimum in each sample of the m magnitudes and the number of times N the minimum appears. The result appears at the read only memory RM₁ whose output is the weight function represented by K bits. The possible values for the weight function are preset according to the aforementioned table. In this regard, the determinations are based on equations (3) or (4) to follow.

The determination of the minimum value of m positive numbers and the number of occurrences of the minimum value is done in the weight function circuit WF_(J) as shown in FIGS. 5 and 6. In this case Q=3. The quantized received samples are represented by the 3-bit number a₀ a₁ a₂ and the hard decision on the sample is a₀. Hence a₁ a₂ represent the magnitude of the sample. The minimum of the magnitudes of m samples is M₁ M₂. The a₁ 's of the numbers are logically ANDed to obtain the M₁ of the minimum value. M₂ of the minimum value is established as follows.

If M₁ is 1, logically AND the a₂ 's to obtain M₀. On the other hand, if M₁ is 0, then logically AND on the a₂ 's of those components whose a₁ are 0. When M₁ is 1, then A₁ to A_(m) (the output of the gates XR₁ to XR_(m) ) are all 0's (since all the a₁ 's are 1) and hence the output of the OR gate following the A₁ to A_(m) is the corresponding a₂. These are logically ANDed to get M₂. Hence the corresponding A₂ passes through to the final AND gate only if an a₁ is an 0. Otherwise, a 1 is passed to the final AND gate AD₂. To count the number of elements that are equal to the minimum, it is noted that any A₁ to A_(m) serves as a flag to indicate if a₁ is equal to the corresponding M₁ or not. That is, if A₁ to A_(m) are all 0, then the i-th a₁ is equal to M₁. The XOR gates Xr₁ to Xr_(m) create a similar flag X₁ to X_(m) to indicate if a₂ is equal to M₂ or not. NOR gates Nr₁ to Nr_(m) execute logical NOR operations on X₁ to X_(m) and A₁ to A_(m) to obtain U₁ to U_(m) which indicates if M₁ M₀ is equal to a₁ a₂ or not. The values U₁ to U_(m) are added to the number of minima N.

Another embodiment of the invention appears in FIGS. 14 and 15 for obtaining weight functions in soft decision decoding of a rate k/n threshold decodable convolutional code.

In FIGS. 14 and 15, the quantizing and storage CS₁ performs the functions of demodulator DE₁ and buffer SB₁, while a register RE₁ corresponds to the parity generator PG₁. The unit UN₁ supplies the generator GW₁ corresponding to WG₁. In FIG. 15, a set of full adders AF and comparators OC form output bits i_(k).

The Invention is based upon the following general considerations. It should be noted that the symbols in the following may not conform to those previously used.

Denote a parity (or syndrome), determined from the binary hard decisions of the components of an error correction code by

    B=r.sub.1 ⊕r.sub.2 ⊕. . . ⊕r.sub.m,            (1)

where the symbol ⊕ represents binary XOR operation. Further, denote by p_(i) the probability that the hard decision r_(i) is in error, given that the corresponding quantized (to Q bit representation) analog sample is y_(i). Since one of the Q bits is used to represent the hard decision r_(i), the remaining (Q-1) bits are used to represent the absolute value of the sample y_(i). The possible values |y_(i) | are denoted 0, 1, . . . , (2^(Q-1) -1), where the notation |x| denotes the absolute value of the real number x . Denote by W the soft decision weight function of B involved in the soft decision decoding of the error correction code.

The previously known simplified weight function uses only the "least reliable" component (in other words, the component with the smallest magnitude) of B. See the aforementioned article by Tanaka et al. Though this method of determining W gives good coding gain for codes with small m, it fails to give good coding gain when m is large.

The invention uses not only the least reliable component of B, but also the number of times it occurs in the parity B in determining the corresponding weight W. This can be written as:

    W=F(|y.sub.min |, N)                     (2)

where

|y_(min) |=minimum of {|y_(s) |; 0<s<(m+1)}

N is the number of elements y_(t) such that

    |y.sub.t =|y.sub.min |, 0<t<(m+1) (3)

The function F(|y_(min) |, N) can be chosen to be one of several functions. Some possible choices are: ##EQU1## where the function

    g(|y.sub.min|)

is given by

    (1-2p(|y.sub.min |))

and K is a positive constant.

The expression p(|y_(min) |) represents the probability of an error given that the (Q-1) bit representation of the magnitude of the received sample is |y_(min) |. This appears in the book Threshold Decoding, by J. L. Massey, published by MIT Press, Cambridge, Massachusetts, 1963. ##EQU2## when 0<|y_(min) |<2.sup.(Q-1) -2, and ##EQU3## when |y_(min) |=2.sup.(Q-1) -1.

The function φ(x) is given by ##EQU4## In (4), E_(s) is the channel symbol energy in BPSK transmission, N₀ is the power spectral density of the additive white Gaussian noise, and Δ is the step size of the uniform quantizer and is chosen without loss of generality to be ##EQU5## where R is the chosen range of the absolute value of the received samples.

The general considerations behind the read-only-memory (ROM) are as follows. Assuming that the demodulator output is quantized to 3 bits for the purpose of soft decision decoding, the reliability of any sample is represented by either 0, 1, 2, or 3. Further assuming that the parameter Δ, as defined in equation (7), is equal to 0.3(E_(s)).sup.(1/2) then equation (4) gives ##EQU6##

Assuming that

    10 log.sub.10 (E.sub.s /N.sub.0)=3 dB,

then p(0)=0.2398, p(1)=0.0296, p(2)=0.003, and p(3)=0.00013. Now the weight W is determined by using Equation (3a). For the values of the minimum reliabilities and the values N in Table 1, the first computed values are, from top to bottom in Table 1, 0.0638, 0.1232, 0.2412, 0.5011, 0.9156, 1.0396, 1.215, 1.516, 1.9195, 2.0445, 2.2205, 2.5216, 3.2195. The value of K is then chosen to normalize the values that W can take. In Table 1, the value K is chosen equal to the inverse of the minimum value 0.0638, which allows the other values to come close to some positive integers to facilitate the easy implementation of the ROM. Since the largest value of the normalized weight is 50, only 6 bits are needed to represent normalized W. Hence the size of the ROM is 13*6=78 memory locations.

According to another embodiment, a further simplification occurs when the blocklength of a block code is large, or when the constraint length of the convolutional code is large and when the signal-to-noise ratio is low to moderate. A weight function circuit embodying this principle appears in FIG. 16. In such a case, instead of determining the |y_(min) | from m elements each having a (Q-1) bit representation, it is assumed that |y_(min) | is 0 and only the number of components in the parity equation (1) with magnitude 0 are counted. This simplifies the decoder a great deal. Thus when quantizing the samples to be used in soft decision decoder, it is sufficient to store the hard decision and if the magnitude of the sample is 0 or not.

The circuit of FIG. 16 replaces those of FIGS. 5 and 6 and receives the same inputs. Here, however the m* (Q-1) inputs are not regrouped from the m groups of Q-1 inputs to the weight function circuits of FIG. 4. Rather the inputs remain grouped in as m groups of (Q-1) inputs a₁ a₂. NOR gates NR₁, NR₂ . . . NR_(m) each receive inputs a₁ and a₂ and apply them to adder DD₁. The latter is the same as that of FIG. 6. The ROM RM₁ operates on the same basis with 0 inputs for M₁ and M₂.

The extra coding gain that can be obtained by using this weight function is substantial when the block code has large block length, or, when the convolutional code has large constraint length (and/or high rate). It is easy to implement and does not have the complexity of the exact weight function.

In other embodiments of the invention, the soft decision decoder output is either fed back to itself, i.e. the decoder input, or fed forward to a separate decoder. The output of the soft decision decoder can be either hard decisions or soft decisions.

FIG. 17 shows hard decision output of the soft decision decoder being fed forward to a hard decision decoder. In FIG. 17, the decoder DE₂ replaces the soft decision decoder DE₁ in the circuits of FIGS. 1, 8, 11, and 12. The decoder DE₂ includes the decoder DE₁, a buffer BU₂ to store the output of the decoder DE₁, and a hard decision decoder HD₁. The hard decision decoder HD₁ takes the output of the soft decision decoder DE₁ stored in the buffer BU₂ and subjects it to hard decision decoding to form the output of the decoder DE₂.

FIG. 18 corresponds to FIG. 17 but substitutes a decoder DE₃ in which the hard decision decoder HD₁ is replaced with a soft decision decoder SD₁, for example a decoder corresponding to DE₁.

FIG. 19 shows a decoder DE₄ which is another form of the decoder DE₂ in FIG. 17. The decoder DE₄ is identical to the decoder DE₁ except for omission of the connection between the last stage of shift register SR₁ to the select circuit SE₁ of FIGS. 3 and 8. Instead the output of the soft decision decoder DE₁ is fed back to the input of the same soft decision decoder at the shift register SR₁ for the hard decisions. Here the decoded output C_(m) from the comparator CO₁ of FIGS. 2 and 8 passes not only to the output circuit OC₁, but also feeds back to the select circuit SE₁ at the input of the hard decision shift register SR₁ of FIGS. 3 and 8. This feedback replaces the feedback in FIGS. 3 and 8 from the last stage of the shift register SR₁ to the select circuit SE₁. This arrangement improves the resulting decoding. The circuit CT₁ includes the elements RC₁, RC₂, WF_(i), XO_(i), B_(i) (i=0 . . . J), MC₁, FA₁,etc. in FIGS. 2 to 4 and 8.

FIG. 20 shows a decoder DE₅ which is another form of the decoder DE₃ in FIG. 18. The decoder DE₅ is identical to the decoder DE₄ except for the omission of the connection from the last stage of the register SR₂ to the select circuit SE₂. Instead in FIG. 20, an absolute value generator AG₁ produces the absolute value of the output F from the full adder FA₁ in FIGS. 2 and 8. A scaling circuit SC₁ divides the absolute value by J+1 and feeds the divided value to the select circuit SE₂ at the input to the soft decision shift register SR₂ in FIGS. 4 and 8. This feedback replaces the feedback in FIGS. 4 and 8 from the last stage of the shift register SR₂ to the select circuit SE₂. This arrangement further improves the resulting decoding.

While embodiments of the invention have been described in detail, it will be evident to those skilled in the art that the invention may be embodied otherwise. 

What is claimed is:
 1. An apparatus for processing a stream of data, comprising:first generating means for generating a set of hard decisions and a set of soft decisions from the stream of data; means for forming a plurality of first subsets from the set of hard decisions parity generating means for generating a set of parities from a plurality of first subsets of said set of hard decisions; means for forming a plurality of second subsets from the set of soft decisions; weight function generating means for generating a plurality of weight functions from said plurality of second subsets of the set of soft decisions based on how many times a given one of said soft decisions occurs in each second subset, and correcting means for producing a corrected data stream with said weight functions and said parities.
 2. An apparatus as in claim 1, wherein:said first generating means includes means for quantizing said stream of data into multiplicities of bits each multiplicity having a most significant bit and bits of lesser significance; said first generating means includes means for generating each of said hard decision from the most significant bit; and said first generating means includes means for generating said soft decisions form the lesser significant bits.
 3. An apparatus as in claim 1, wherein:said parity generating means includes means for logically combining the hard decisions of said first subsets; and said correcting means for producing a corrected data stream includes means for weighting the parities with the weight functions, means for adding the weighted parities, means for comparing the added weighted parities to a threshold for producing said corrected set of bits.
 4. An apparatus as in claim 3, wherein:said first generating means includes means for forming the set of hard decisions and the set of soft decisions, and means for cyclically shifting the set of hard decisions and the set of soft decisions to create new sets of hard decisions and soft decisions.
 5. An apparatus as in claim 3, wherein:said first generating means includes means for generating a hard decision and a soft decision from the same data element in a stream of data producing a set of soft decisions that correspond to the set of hard decisions; said parity generating means and said weight function generating means form a corresponding plurality of first functions form the subsets of hard decisions and a plurality of second function from the subsets of soft decisions.
 6. An apparatus as in claim 1, wherein:said soft decisions represent reliabilities and are defined by two bits with values 00, 01, 10 and 11, wherein a reliability increases as the value of the bits increases.
 7. An apparatus as in claim 6, wherein:said soft decision is 00 in each of said second subsets.
 8. An apparatus as in claim 1, wherein:said soft decisions in each second subset include a given minimum value soft decision, ad the given soft decision is the minimum value soft decision in each second subset.
 9. An apparatus as in claim 8, wherein each soft decision has two bits, one of said bits being a more significant bit and the other bit being a lesser significant bit said weight function generating means for establishing a given minimum value soft decision from each second subset and how often the given minimum value soft decision occurs in each second subset includes:means for logically ANDing a set of more significant bits of two bits representing the soft decisions of a second subset to obtain a first result; logic means responding to the first result being 1 for logically ANDing the lesser significant of the two bits representing the set of soft decisions of the second subset to obtain a second result; said logic means responding to the first result being zero for logically ANDing the lesser significant of the two bits representing the soft decisions of the second subset whose more significant bit is a 0; means for determining whether each of the more significant of the two bits representing the soft decisions of the second subset is equal to the first result and for determining whether each of the lesser significant of the two bits representing the soft decisions of the second subset is equal to the second result; and means for logically NORing the determining of said determining means to obtain a plurality of indicators; and means connected to the means for logically NORing for adding the indicators.
 10. An apparatus as in claim 1, wherein:a predetermined look-up table receives said soft decisions and how many times the given one of the soft decisions occurs in each of said second subsets to obtain a weight function.
 11. An apparatus as in claim 1, further comprising:decoding means coupled to said correcting means for further decoding said corrected data stream to produce a further corrected data stream.
 12. An apparatus as in claim 1, further comprising:feedback means for feeding the corrected data stream of said correcting means to said parity generating means for further decoding the corrected data stream.
 13. The method of processing a stream of data, comprising:generating a set of hard decisions and a set of soft decisions form the stream of data forming a plurality of first subsets from said set of hard decisions; generating a set of parities from each of first subsets of said set of hard decisions; forming a plurality of second subsets from said set of soft decisions; generating a plurality of weight functions from said plurality of second subsets of the set of soft decisions, said generating of each weight function includes determining how many times a given one of the soft decisions occurs in each second subset; and producing a corrected data stream with said weight functions and said parities.
 14. The method as in claim 13, wherein:said steps of generating said sets of hard decisions includes quantizing said stream of data into a plurality of bits each plurality having a most significant bit and bits of lesser significance; and each of said hard decisions is generated from the most significant bit; and said soft decisions are generated from the bits of lesser significance.
 15. The method as in claim 13, wherein:said step of generating a set of parities includes logically combining the hard decisions of said first subsets; and said step of producing a corrected data stream includes weighting the parities with the weight functions, adding the weighted parities, comparing the added weighted parities to a threshold to obtain results, the results of said comparisons being the said corrected set of bits.
 16. The method as in claim 15, wherein:said step of generating a set of hard decisions and a set of soft decisions includes the substeps of: forming a set of the hard decisions and a set of the soft decisions, cyclically shifting the set of hard decisions and cyclically shifting the set of soft decisions to form new sets of hard decisions and set of soft decisions.
 17. The method as in claim 15, further comprising:further decoding said corrected data stream to produce further corrected data streams.
 18. The method as in claim 15, wherein:said generating step for generating a set of hard decisions and a set of soft decisions includes generating a hard decision and a corresponding soft decision form the same data element in a stream of data and producing a set of soft decisions that correspond to the set of hard decisions; said parity generating step and said weight function generating step form a corresponding plurality of first functions form the subsets of hard decisions and a plurality of second functions from the subsets of soft decisions.
 19. The method as in claim 13, wherein:the soft decisions have values represented by 2 bits having magnitudes, namely 00, 01, 10, and 11, wherein a value increases as the magnitude of the bits increases.
 20. The method as in claim 19, wherein:said soft decisions having minimum values, said step of generating weight functions includes establishing minimum soft decisions having minimum values; said given soft decision is the minimum soft decision in each second subset.
 21. The method as in claim 20, wherein each soft decision measure has two bits, one of said bits being a more significant bit and the other bit being a lesser significant bit the step of a minimum soft decision from each second subset and the number of times the minimum soft decision occurs in each second subset includes:logically ANDing the set of more significant of the two bits representing the reliabilities of the members of a second subset to obtain a first result; if the first result is 1, logically ANDing the lesser significant of the two bits representing the soft decisions of a second subset to obtain a second result; if the first result is zero, logically ANDing the lesser significant of the two bits representing the soft decisions of the second subset whose more significant bit is a 0; determining whether each of the more significant of the two bits representing the soft decisions of the second subset is equal to the first result; determining whether each of the lesser significant of the two bits representing the soft decisions of the second subset is equal to the second result; and logically NORing the determining of said determining steps to obtain a plurality of indicators, and adding the logically NORed indicators.
 22. The method as in claim 20, wherein:said minimum soft decision and how many times the minimum soft decisions occurs in each said second subset is in put to a pre-determined look-up table to obtain a weight function.
 23. The method as in claim 13, wherein:said given soft decisions is set at 00 in each of said second subsets.
 24. A data transfer system, comprising:a source of a stream of data; receiver for receiving the stream of data, including a demodulator, an error corrector, and an output; said demodulator including generating means for generating a set of hard decisions and a set of soft decisions from the stream of data; said error correcting means including means for forming a plurality of first subsets from the set of hard decisions; said error corrector including parity generating means for generating a set of parities from a plurality of first subsets of said set of hard decisions; said error corrector including means for forming a plurality of second subsets form the set of soft decisions; said error corrector including weight function generating means for generating a plurality of weight functions from said plurality of second subsets of the set of soft decisions based on how many times a given one of said soft decisions occurs in each second subset, and said output including correcting means for producing a corrected data stream with said weight functions and said parities.
 25. A system as in claim 24, further comprising:decoding means coupled to said correcting means for further decoding said corrected data stream to produce a further corrected data stream.
 26. A system as in claim 24, further comprising:feedback means for feeding the corrected data stream of said correcting means to said parity generating means for further decoding the corrected data stream of said correcting means. 